Generalized Hooke Law for Relativistic Membranes and p-branes

TL;DR

This paper explores the elastic properties of relativistic membranes and p-branes, reducing their complex equations to classical anharmonic media models, analyzing integrability, and constructing some exact solutions.

Contribution

It introduces a reduction of relativistic membrane and p-brane equations to classical anharmonic media equations and discusses their integrability and solutions.

Findings

Reduced brane equations to anharmonic media models

Discussed integrability of the equations

Constructed some exact solutions

Abstract

The character of elastic forces of relativistic membranes and $p$-branes encoded in their nonlinear equations is studied. The toroidal brane equations are reduced to the classical equations of anharmonic elastic media described by monomial potentials. Integrability of the equations is discussed and some of their exact solutions are constructed.